The rate of effusion - that is, leakage of a gas through...

The rate of effusion - that is, leakage of a gas through tiny cracks-is proportional to $v_{\mathrm{rms}} .$ If tiny cracks exist in the material that's used to seal the space between two glass panes, how many times greater is the rate of He leakage out of the space between the panes than the rate of Xe leakage at the same temperature? (a) 370 times; (b) 19 times; (c) 6 times; (d) no greater-the He leakage rate is the same as for Xe.

The rate of effusion - that is, leakage of a gas through tiny cracks-is proportional to $v_{\mathrm{rms}} .$ If tiny cracks exist in the material that's used to seal the space between two glass panes, how many times greater is the rate of He leakage out of the space between the panes than the rate of Xe leakage at the same temperature? (a) 370 times;
(b) 19 times; (c) 6 times; (d) no greater-the He leakage rate is the same as for Xe.

Key Concepts

Relationship between Molecular Mass and Speed

The molecular mass of a gas directly influences its molecular speed; lighter molecules such as helium travel faster on average than heavier molecules like xenon at a given temperature. Since the rate of effusion is proportional to v_rms, gases with lower molecular mass will effuse more quickly than those with higher molecular mass.

Kinetic Molecular Theory

The kinetic molecular theory provides a framework for understanding the behavior and properties of gases. It explains concepts such as molecular speed distribution, pressure, temperature, and how these factors contribute to phenomena like diffusion and effusion. This theory underpins the derivation of v_rms and helps explain why lighter gases effuse at higher rates.

Effusion

Effusion is the process by which gas molecules escape through small openings or cracks without significant collisions among themselves. The rate of effusion is influenced by the speed of the gas molecules, as faster molecules are more likely to exit through tiny openings. This concept is a key part of gas behavior studies in the kinetic molecular theory.

Root Mean Square Speed (v_rms)

The root mean square speed is a measure of the average speed of gas molecules in a sample. It is derived from the kinetic molecular theory and is given by the equation v_rms = sqrt(3kT/m), where k is the Boltzmann constant, T is the absolute temperature, and m is the molecular mass. This concept is crucial for understanding how molecular mass influences the rate at which gases effuse.

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